Phantom relaxation rate of the average purity evolution in random circuits due to Jordan non-Hermitian skin effect and magic sums

Žnidarič, Marko (avtor)

Phantom relaxation is relaxation with a rate that is not given by a finite spectral gap. Studying the average purity dynamics in a staircase random Haar circuit and the spectral decomposition of a nonsymmetric matrix describing the underlying Markovian evolution, we explain how that can arise out of an ordinary-looking spectrum. Crucial are alternating expansion coefficients that diverge in the thermodynamic limit due to the non-Hermitian skin effect in the matrix describing the average purity dynamics under an overall unitary evolution. The mysterious phantom relaxation emerges out of localized generalized eigenvectors describing the Jordan normal form kernel, and, independently, also out of interesting trigonometric sums due to localized true eigenvectors. All this shows that when dealing with non-Hermitian matrices it can happen that the spectrum is not the relevant object; rather, it is the pseudospectrum or, equivalently, a delicate cancellation enabled by localized eigenvectors.

• Jezik: Angleški jezik
• Ključne besede: quantum mechanics
• Vrsta gradiva: Članek v reviji
• Tipologija: 1.01 - Izvirni znanstveni članek
• Organizacija: FMF - Fakulteta za matematiko in fiziko
• Različica publikacije: Objavljena publikacija
• Datum objave: 01.09.2023
• Leto izida: 2023
• Št. strani: Str. 033145-1-033145-17
• Številčenje: Vol. 5, iss. 3
• PID: 20.500.12556/RUL-155002
• UDK: 530.145
• ISSN pri članku: 2643-1564
• DOI: 10.1103/PhysRevResearch.5.033145
• COBISS.SI-ID: 188725251
• Datum objave v RUL: 13.03.2024

Gradivo je del revije

• Naslov: Physical review research
• Založnik: American Phyisical Society
• ISSN: 2643-1564
• COBISS.SI-ID: 32822823

Licence

• Licenca: CC BY 4.0, Creative Commons Priznanje avtorstva 4.0 Mednarodna
• Povezava: http://creativecommons.org/licenses/by/4.0/deed.sl
• Opis: To je standardna licenca Creative Commons, ki daje uporabnikom največ možnosti za nadaljnjo uporabo dela, pri čemer morajo navesti avtorja.

Sekundarni jezik

• Jezik: Slovenski jezik
• Ključne besede: kvantna mehanika

Projekti

• Financer: ARRS - Agencija za raziskovalno dejavnost Republike Slovenije
• Številka projekta: J1-4385
• Naslov: Kvantna večdelčna fizika in nehermitskost

• Financer: ARRS - Agencija za raziskovalno dejavnost Republike Slovenije
• Številka projekta: P1-0402
• Naslov: Matematična fizika